8. The Atomic Bond

by Tom Gilmore
Copyright 2018
All graphics by Tom Gilmore

Atomic Symmetry Law

In the Geocubic Model single Protons are isolated inside spherical force surfaces (Neutrinos).  The Spheres are compressed into cubic containment.

The arrangement of Spheres in the cube is dictated by the forces of order and symmetry. 

The Symmetry Law is that the internal arrangement of the Spheres in the cube
Must be symmetrical in 2-dimensions, but
Cannot be symmetrical in all 3-dimensions.

Atomic Form Emulation

Each atomic Element has a specific number of Protons (and thus Spheres), and this is termed the Atomic Number.  The syntax used on the Geocubic articles to identify atoms is ElementName(n), where (n) is the Atomic Number.  For example Carbon(6).

The Protons of an atom are bound together by an energy deficit taken from the individual Protons (this is termed the “Nucleon”).  This Nucleonic binding force is weaker than the Symmetry demand, and consequently those Elements which cannot meet the Symmetry demand are forced to either transfer out or receive Protons (Spheres) in order to arrive at an allowed arrangement. 

In transferring Spheres, the effective Atomic Number of the atoms change, but the atom retains its original identity through the unchanged Nucleon.  Because of the transfers, the internal Sphere arrangement of the atoms involved in the bonding have changed, and the atoms emulate the form of the Element of the resultant number of Spheres.  For example Carbon(6)Helium-form(2) is a Carbon atom emulating a Helium atom (by transferring out 4 Spheres).

Valence is the integer count of potential Sphere transfers for an Element.  There are two types of valence: required and dictated.  Elements with no valid arrangement are required to loan or borrow to reach a valid Element-form.  Some Elements with valid (ordered) arrangements will move (chemically react) to other ordered Element-forms if in bonding the result is lesser energy,  In general, the conditions required to initiate a chemical reaction can be considered as a catalyst (which dictates the reaction).

The Law of Lesser Energy
If atomic bonds of lesser energy can form, they must form.

Atomic Bonding Force

In the Geocubic Model’s illustrations of atomic bonding, the atomic bonds are indicated by transferred Spheres marked with arrows.  The sent Spheres are shown as clear circles, and the received Spheres are shown grayed. 

Spheres can only transfer between adjacent atoms.  In the matrix of cubes, each cube is surrounded by 26 adjacent cubes.  Spheres transferred to adjacent atoms remain bound to the atom of their origin by the Nucleonic binding force. 

The diagram above shows the molecule of water (H2O) with the opposite components of the bonding force color coded.  The stronger Symmetry Demand transfers the Spheres (red arrows), while the weaker Nucleonic force binds the borrower atom to the loaner atom (violet arrows).

Single Sphere transfers generally occur at the cube corners.  When two Spheres transfer it is at the cube edges, and when 3 or 4 Spheres transfer it is at the cube faces.  There can be multiple transfers from a single atom to adjacent atoms, but each transfer is limited to 4 Spheres.

Precluded Order and Absent Order

Hydrogen(1) and Oxygen(8) violate the absolute order exclusion (precluded order), as can be seen crossed off in the graphic below, in that they have identical symmetry in all 3 dimensions.


Helium(2) and Neon(10), shown above, are symmetrical as demanded, but are not symmetrical in all 3 dimensions.  They both are inert Elements.  Inert Elements are not subject to atomic bonding.

Hydrogen and Oxygen both always occur either in a diatomic molecule or are incorporated in some other molecule that eliminates the precluded full symmetry. 

Shown below is the diatomic Hydrogen bond, where one Hydrogen atom is empty (Void), and the other Hydrogen contains 2 Spheres, thus emulating the inert Helium-form(2).  Hydrogen is the only Element nuclide that can be Void of Spheres, but it is averse to this condition, forcing the Hydrogen molecule to switch back and forth which atom is Void.  The Hydrogen molecule will readily split apart to join in the atomic bonds of another molecule, even if the Hydrogen atoms transferred are Void in that molecule, but the aversion to being Void causes an intermolecular attraction.  See articles on Acids and Genetic Coding for examples of Void linkages.

The Hydrogen molecule in Geocubic syntax is
[Hydrogen(1)Helium-form(2) + Hydrogen(1)Void(0)], or in shorthand
[H(1,2)+H(1.0)].  The square brackets are used to enclose the atoms of a molecule.

The Hydrogen molecule is an example of what is conventionally termed a “single-covalent” bond, meaning that the bond goes in either direction between all the atoms involved. 

The conventional interpretation of the structure of the Oxygen molecule is called “double covalent”, and is conceived as a sharing (switching back and forth) of 2 Proton/Neutrino pairs, one pair from each oxygen, as illustrated below.

To Summerize:

In bonding, atoms change their internal arrangements, and take on the characteristics of the Element they emulate, but the original Elements are still intact, they have only added or reduced through borrowed Spheres, and are bonded by this borrowing. 

The Elements Hydrogen and Oxygen cannot exist separately due to their absolute symmetry (this is called precluded order).  Some other Elements, such as the alkali and halogen Elements cannot exist separately due to not having a possible symmetrical Sphere arrangement in 2-dimensions (this is called absent order). 

The Tetrahedral Bond

The tetrahedral bond is the most common bonding form.  A tetragon has 4 equal triangular faces, as diagramed in 2 mirrored forms below left.  The middle illustration shows a cube added to an outline of the tetragon, and the vertices are marked with black dots.  On the upper and lower cube, these dots show the 2 chiral (mirrored) tetrahedral bonding corners.  To the right, the Geocubic Model shows a central cube is surrounded by 4 cubes located at the corners corresponding to the tetrahedral corners (black dots).

The Alkane Gas Series

An alkane gas consists of only Carbon and Hydrogen atoms with tetrahedral "single-covalent" bonds (hereafter termed “bi-directional”). 

Methane consists of one Carbon(6) atom bonded to 4 Hydrogen(1) atoms in a tetrahedral arrangement (bonding to 4 opposite corners).
In the diagram below, the Methane molecule is shown in the two forms produced by the bi-directional transfer. 
The Carbon atom is shown with bold front edges of the cube.

To the left above, there are 4 transfers into the Carbon(6) atom, and to the right there are 4 transfers out of the Carbon(6) atom. 

Beginning with Methane, the Alkane series of hydrocarbons is incrementally adding Carbon(6) atoms, and for each added Carbon(6) atom, 2 Hydrogen(1) atoms are added.  This is because the Carbon atoms link in a bond chain, replacing the need for 2 Hydrogen atoms per Carbon link   Due to the overall reduction of Hydrogen-to-Carbon proportions, the energy of the hydrocarbon declines with the increase of Carbon atoms. 

Methane – 1 Carbon
Ethane – 2 Carbons
Propane – 3 Carbons
Butane – 4 Carbons

The chemical formula of Ethane is C2H6  or (H3C- CH3 ).  For Ethane (shown below) the bi-directional transfer is indistinguishable (merely flipping over the molecular structure).


An alternate Geocubic diagram form (not showing Spheres) of Ethane is shown to the right above.  It uses opaque cubes labeled with the atomic number of the Element, with the resultant Element-form in red.  Arrows that are obscured in 3-dimensions are shown in grey.

Propane consists of 3 Carbon atoms bonded with 8 Hydrogen atoms.  Notice that the linked Carbon atoms alternate between Neon-form(10) and Helium-form(2).  This alternation between linked Carbon atoms is dictated by the necessity of sending 4 Spheres or receiving 4 Spheres.

As can be seen in the diagram above of one of the two bi-directional transfers of Propane, the left and right most Carbon atoms bond with 3 Hydrogen atoms, but the central Carbon atom only needs 2 Hydrogen atoms to reduce to Helium-form(2), because it transfers the other 2 Spheres to the 2 adjacent Carbon atoms. 


The linked Carbon chain is extended to 4 Carbon atoms in Butane (H3C-CH2-CH2-CH3 )

An isomer is an alternate arrangement of a molecule with the same mix of atoms.  Methane (CH4), Ethane (H3C - CH3), and Propane (H3C - CH2 - CH3) have only one arrangement (no isomers).  In the alkane molecule the Carbon atoms are bonding in tetrahedral chains.  With 4 Carbon atoms it becomes possible for alternate corner connections to form.  A restriction of the isomer is that all the Carbon atoms must alternate between Neon-form(10) and Helium-form(2).  There is only one Butane isomer, called Isobutane (diagrammed below).  Instead of forming a zig-zag chain (as shown above), the 4th Carbon attaches to the middle Carbon.  All 3 Carbon atoms at the end points must bond with 3 Hydrogen atoms, but in this isomer the center Carbon links to 3 other Carbon atoms and this reduces the need to only 1 Hydrogen atom for the central Carbon (thus the count of Hydrogen atoms remains unchanged in the isomer).

As the number of Carbon atoms increase the possible alternate Carbon linkages increase exponentially.  With 5 Carbons there are 3 isomers, with 6 Carbons there are 5, with 12 Carbons there are 355, and with 32 Carbons there are 27,711,253,769 isomers.

Interlaced Tetrahedral Bonding of Diamond

The Tetrahedral Lattice

The Diamond macro-molecule is created from Carbon(6) atoms under intense pressure and temperature. 

Diamond has 2 interpenetrating tetrahedral lattices.  There are no bonds between the 2 lattices, but they are offset to each other in the cubic matrix, and thus interlock.

There are 2 chiral forms of the tetrahedral unit-cell.  The chiral diagram is repeated here for reference. 

The Tetrahedral Carbon Bonds

Because in the tetrahedral lattice the unit-cells overlap, the base and mirrored unit-cells alternate (centered at each adjacent atom).  The bonded form of adjacent atoms alternate between Neon-form(10) and Helium-form(2).  Each Carbon(6) that takes Neon-form(10) receives 1 Sphere from the 4 Helium-form(2) atoms surrounding it, and each Carbon(6) that takes Helium-form(2) gives 1 Sphere to each of the 4 Neon-form(10) atoms around it.  This is illustrated below, only showing the unit-cell bonds.

The result is that the Neon-form(10) Carbon atom takes on 4 Spheres, increasing from 6 Spheres to 10 Spheres, and the Helium-form(2) Carbon atom gives up 4 Spheres, reducing from 6 Spheres to 2 Spheres.

Although the atomic bonds make Diamond solid, the Neon and Helium forms are inert gas forms, and this makes the Diamond transparent (impurities introduce colors).  The interpenetrating lattices make Diamond hard.

Diamond Faults

The designation of Base and Mirrored is arbitrary, and refers to the chiral corner attachments, not to the bonded form of the central atom of the unit-cell.  A Diamond lattice can form with the Neon-form(10) centered in the base chiral unit-cell (as shown above), or with the Helium-form(2) in the base chiral unit-cell.  The two different lattice types are listed below. 

Base -- Neon-form      à Mirrored -- Helium-form

Base – Helium-form   à Mirrored – Neon-form

The interpenetrating lattices are independent in regard to whether Neon or Helium forms are centered in the base chiral unit-cell (the lattices can be the same or opposite).  However, the Diamond lattices can have local seed points where the lattice type originates. Where opposite seeded types meet, the bonds cannot continue (because adjacent atoms at the meeting will be the same form, either forms Neon-to-Neon, or forms Helium-to-Helium).  Such breaks in the lattice bonding can be held together by the other interpenetrating lattice, but they represent a weak fault where the Diamond can fracture.

The Conventional Diamond “Unit-Cell”

Conventional molecular models use Spheres connected by rods (instead of cubes connected by corners).

The conventional “unit-cell” is represented as shown below, actually being 4 linked base unit-cells.  The numbers are added to the conventional diagram to identify the center atoms of the 4 interconnected base unit-cells.  With the arbitrary size of the lattice of the conventional “unit-cell”, there is no complete mirrored unit-cell depicted.

The Geocubic Model shown below is exactly the same arrangement as the conventional representation above, substituting corner-connected cubes for the Spheres connected by rods.  It reveals that the single cube in the conventional diagram above is actually a 5x5x5 matrix of cubes. 


The Linked Unit-Cells

To aid visualizing the repeated base unit-cells in the tetrahedral structure, 3 linked base unit-cells are shown below using color-coding.

The lattice below color-codes 5 mirrored unit-cells.  The included base unit-cell is circled.

The Interpenetrating Form

The diagram below shows the 2 interpenetrating tetrahedral lattices, with one of the lattices darkened. 


The conventional coordination number is shown as (4,4), due to the 2 interpenetrating tetrahedral lattices, but it is understood that the number is actually 8 in terms of the number of immediately surrounding atoms. 

Macro-Molecule Boundaries

Diamond is an unending macro-molecule.  The issue is that the atoms at the surface boundaries of Diamond would require a continuation of the molecule to complete the transfers of Spheres necessary to reach the inert forms.  The Carbon(6) atoms are alternating between Helium-form(2) and Neon-form(10).  The Neon-form requires receiving 4 Spheres, and the Helium-form requires sending 4 Spheres, and this is done with one Sphere at each bond, with each Carbon atom surrounded by 4 Carbon atoms.  At the boundary atoms, the transfers are incomplete by from 1 to 3 Spheres.  To accommodate this, Hydrogen(1) atoms attached at the boundaries where, if the molecule were extended, a Carbon atom would attach.  The Hydrogen(1) would either receive a Sphere to increase to Helium-form(2), or send a Sphere, emptying (Voiding) the cube, depending on which form of Carbon it attaches to.

Index of all Articles by Tom Gilmore